About the Author/RALPH SHOBERG
Ralph S. Shoberg is the Technical Director of PCB Load & Torque, Inc., a manufacturer of load cells,
torque transducers, and fastening technology measurement equipment.
Shoberg has 30 years expereince in test, measurement, and control of the threaded fastener
tightening process. He has been granted numerous U.S. and international patents for transducer and
instrumentation inventions. Shoberg helped create the first electronic strain-gage transducer based
monitor and control system for automated fastener assembly. He is a frequent lecturer on the design
and analysis of bolted joints, has contributed to a number of threaded fastener handbooks, and is a
frequent contributor to fastener industry-based periodicals.
Advanced Bolt Torque Audit Yields
Bolt Tension Data
Torque-Angle Signature Analysis & M-Alpha Audit Method
Auditing the performance of tightened bolted joints has
long been a priority of quality and assembly
personnel in the manufacturing and maintenance fields.
There have been many methods developed over the
past 40 years to determine the “residual torque” on a
tightened fastener and this value is used as a measure of joint integrity. Each of these techniques is a
practical method of determining the torque remaining
in the joint or the capability of the installation tool; however the true object of tightening a fastener is to produce a clamping load in the joint that will create a reliable assembly. The object of tightening a fastener is
to achieve a tension load on the fastener that clamps
the bolted components with sufficient force to create a
reliable assembly.
What is needed is a method of estimating the “residual tension” achieved by a fastener in a bolted assembly (not torque). RS Technologies (a division of
PCB Load & Torque, Inc.) developed and patented an
auditing method known as the “M-Alpha Torque-Tension Audit” to estimate residual clamping load without
having to rely on strain gaging a bolt, using ultrasonic
methods, or using force washers. The ability to estimate both residual torque and residual tension on a
bolted joint is the reason that the “M-Alpha” auditing
process is considered to be a significant technological
breakthrough for fastener tightness technology.
Because the M-Alpha audit method can permit the
user to obtain bolt tension related measurements, it
represents a paradigm shift in the way “torque audits”
can be conducted. Reliable bolted joints must have
the proper clamp force holding the components together. Tension on the fastener is what is needed to
be verified, not installation or “residual torque.”
Theory and Application of the M-Alpha Joint
Auditing Method
The patented M-Alpha joint auditing method is a process of estimating the amount of clamp load on a
threaded fastener using torque-angle signature analysis. The method is based on locating the “Elastic Ori-
gin” and analysis of the torque-angle signature to determine the elastic tightening angle of turn. The angular
displacement (turn) of the fastener stretches the bolt
and compresses the parts being clamped. The elastic
clamping region of the torque-angle signature is the
region where clamping force is directly proportional to
the angle of turn from the “elastic origin.”
The elastic origin is located by projection of the
straight-line portion of the signature curve backwards
to zero torque, or the prevailing torque level in the case
of thread locking interference type of applications.
This principal can be observed when viewing a clamp
load-angle curve (see Figure 1). Once the curve becomes linear, the clamp load will increase at a consistent rate with each angle of rotation. This remains true
until the curve stops being linear due to yielding of the
fastener or the joint.
The amount of preload in the joint determines how
well the joint will function when it experiences working
loads. Insufficient preload is a major cause of fastener
failures, leading to expensive machinery failures, tragic
accidents, personal injuries, and even loss of life.
The torque-angle signature does not directly provide a measure of the fastener tension. However, it
has been verified that for a given bolted joint, properly
qualified, this signature can be used to directly estimate the clamping force on the bolt, as seen in Figure
2. For example, strain gages on a bolt or stud can be
used to simultaneously measure the installation torque
and the bolt tension. By scaling and plotting the mea-
sured torque and tension, shown in Figure 3, it is apparent that both are in direct proportion to each other.
 Step 4: Determine the Elastic Clamping Angle,
measured from the Elastic Origin, as in Figure 6.
The torque and clamp load plots match up precisely
when the ordinates are scaled. This relationship for
the linear portion of the torque-angle curve can be used
to directly calculate the clamp load in the joint. This is
a fundamental characteristic of bolted joints tightened
below the yield point of the bolt or components being
clamped.
Measure the Elastic Clamp Angle from the Elastic
Origin to obtain the final torque value. The clamping
force achieved by the fastener is directly proportional
to the measured Elastic Clamping Angle. Knowing how
the torque-angle signature looks when tightening a fastener helps to understand the M-Alpha Audit method.
Performing the M-Alpha Joint Auditing Method
The objective of the M-Alpha Audit process is the
determine the “Elastic Tightening Angle” for a preciously
tightened fastener. The amount of clamping load in the
joint is directly proportional to the elastic tightening
angle. The process of the torque-angle curve analysis
is shown in Figures 7 through 10 to illustrate the concepts of the “Elastic Origin” and how the “Elastic Tightening Angle” is determined for a given bolted joint.
 Step 1: Tighten the fastener with the specified
torque (as seen in Figure 2, previously) stopping in the
elastic clamping region.
 Step 2: Locate two points on the linear section of
the torque-angle signature curve (Figure 4).
 Step 3: Project a line through the two points to the
zero torque level, locating the Elastic Origin, as depicted in Figure 5.
M-Alpha Torque-Tension Audits
Torque audits typically involve tightening a preassembled joint a small additional angle, usually as
little as five degrees or less and rarely more than ten
degrees.
Traditional audits simply measured the peak torque
values or used a calculation algorithm to more accurately locate a residual torque value as a measure of
the joint integrity. The M-Alpha method allows the residual torque value to be measured, as shown in Figure 7. More importantly, a paradigm concept, the MAlpha audit can provide an accurate estimate of the
residual clamping load on the tightened fastener.
To illustrate the M-Alpha Audit, overlay the audit
signature (Figure 7) with the installation signature (Figure 2) as shown in Figure 8.
The audit signature created by advancing (tighten-
clamping forces on the five lug nuts on a single automotive wheel, or all 20 lug nuts on the four wheels.
To get an accurate estimate of clamping force on a
bolted joint being audited, the relationship between
torque, clamp load, and angle must be experimentally
determined or calculated. A clamp load/degree coefficient can be determined experimentally using stain
gaged bolts, force washers, elongation measurement,
or ultrasonic elongation equipment. Calculations are
easily done using the SR1 Bolted Joint Design/Analysis program. (Note: For more information, visit
www.pcbloadtorque.com).
ing) the fastener a few degrees will simply be a continuation of the torque angle curve on the same linear
slope in the elastic tightening region.
The M-Alpha Audit is accomplished by advancing
the fastener in the tightening direction, projecting a tangent line to the audit signature to locate the elastic
origin, and measuring the angle from elastic origin to
the residual torque point. The residual tension on the
fastener is proportional to the elastic clamping angle
determined by the audit. Multiply the Audit Clamp Angle
by the Angle-Tension Coefficient to estimate the actual tension on the fastener, as seen in Figure 9.
The M-Alpha method can be used to estimate the
relative clamp load in a tightened joint. For this application, the exact elastic tightening angle of clamp force
coefficient does not need to be known. An example of
this application would be to determine the relative
With the M-Alpha Audit, engineers and technicians
have a powerful tool to use in their quest to assure
reliable bolted joints on machinery, steam turbines, gas
turbines, compressors, pumps, electric motors, wind
energy towers, highway signs, bridges, and more.
Reprinted from Distributor’s Link Magazine, Fall 2010